Algebraically, the ordered pair (x, y) becomes (-x, y). In a reflection about the y-axis, the y-coordinates stay the same while the x-coordinates take on their opposite sign. All of the points on triangle ABC undergo the same change to form DEF. Triangle DEF is formed by reflecting ABC across the x-axis and has vertices D (-6, -2), E (-4, -6) and F (-2, -4). Algebraically, the ordered pair (x, y) becomes (x, -y). In a reflection about the x-axis, the x-coordinates stay the same while the y-coordinates take on their opposite signs. The most common cases use the x-axis, y-axis, and the line y = x as the line of reflection. There are a number of different types of reflections in the coordinate plane. This is true for any corresponding points on the two triangles and this same concept applies to all 2D shapes. A, B, and C are the same distance from the line of reflection as their corresponding points, D, E, and F. The figure below shows the reflection of triangle ABC across the line of reflection (vertical line shown in blue) to form triangle DEF. The same is true for a 3D object across a plane of refection. In a reflection of a 2D object, each point on the preimage moves the same distance across the line of reflection to form a mirror image of itself. The term "preimage" is used to describe a geometric figure before it has been transformed "image" is used to describe it after it has been transformed. ![]() When an object is reflected across a line (or plane) of reflection, the size and shape of the object does not change, only its configuration the objects are therefore congruent before and after the transformation. In geometry, a reflection is a rigid transformation in which an object is mirrored across a line or plane. The reflection of a point $(x,y)$ over the x-axis will be represented as $(x,-y)$.Īllan was working as an architect engineer on a construction site and he just realized that the function $y = 3x^+4(-x) -1)$.Home / geometry / transformation / reflection ReflectionĪ reflection is a type of geometric transformation in which a shape is flipped over a line. In that case, the reflection over the x-axis equation for the given function will be written as $y = -f(x)$, and here you can see that all the values of “$y$” will have an opposite sign as compared to the original function. When we have to reflect a function over the x-axis, the points of the x coordinates will remain the same while we will change the signs of all the coordinates of the y-axis.įor example, suppose we have to reflect the given function $y = f(x)$ around the x-axis. How To Reflect a Function Over the X-axis Reflection of a function over x and y axisĪll these types of reflections can be used for reflecting linear functions and non-linear functions.Reflection of a function over y- axis or horizontal reflection.Reflection of a function over x – axis or vertical reflection.Hence, we classify reflections of the function as: Consider the function $y = f(x)$, it can be reflected over the x-axis as $y = -f(x)$ or over the y-axis as $y = f(-x)$ or over both the axis as $y = -f(-x)$. There are three types of reflections of a function. On the other hand, during the reflection of a function, position as well as the direction of the image of the graph is changed while the shape and size remain the same. ![]() ![]() During the translation of a function, only the position of a function is changed while the size, shape, and direction remain the same. The direction of the reflected image or graph should be opposite to the original image or graph.Īs we discussed earlier, there are four types of function transformations, and students often confuse the reflection of a function with the translation of a function. ![]() The one feature that does not match is the direction. Read more Coefficient Matrix - Explanation and Examples
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